In this short chapter, we show that the edge-kstar model exhibits many of the properties of the edge-2star model. In particular: all entropy maximizers are multipodal with a uniform bound on the number of defining parameters; there is a single bipodal phase along the lower boundary of the phase space; near the top of the phase space there is a phase transition between cliquelike and anticliquelike graphs, with two optimal graphons on the curve dividing these regions. We also show that there is a bipodal phase in a model where we constrain an arbitrary positive linear combination of kstar densities. As we will see in Chapter 7, every edge-H model (where H is a fixed graph) is well approximated by an edge-(linear combination of kstars) model. The estimates of this chapter are at the core of the proof of Theorem 7.11, proving the existence of a bipodal phase for all edge-H models.